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New Journal of Physics

Quantum measurements between a single spin and a torsional nanomechanical resonator

Brian D’Urso, M V Gurudev Dutt, Shonali Dhingra, Naufer Nusran

Published Apr 4, 2011• 8 citations
Publisher

Abstract

While the motions of macroscopic objects must ultimately be governed by quantum mechanics, the distinctive features of quantum mechanics can be hidden or washed out by thermal excitations and coupling to the environment. We propose a system consisting of a graphene nanomechanical oscillator (NMO) coupled with a single spin through a uniform external magnetic field, which could become the building block for a wide range of quantum nanomechanical devices. The choice of graphene as the NMO material is critical for minimizing the moment of inertia of the oscillator. The spin originates from a nitrogen-vacancy (NV) center in a diamond nanocrystal that is positioned on the NMO. This coupling results in quantum non-demolition (QND) measurements of the oscillator and spin states, enabling a bridge between the quantum and classical worlds for a simple readout of the NV center spin and observation of the discrete states of the NMO.

DOI
10.1088/1367-2630/13/4/045002

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Though the motions of macroscopic objects must ultimately be governed by quantum mechanics, the distinctive features of quantum mechanics can be hidden or washed out by thermal excitations and coupling to the environment. For the work of this thesis, we tried to develop a hybrid system consisting a classical and a quantum component, which can be used to probe the quantum nature of both these components. This hybrid system quadratically coupled a nanomechanical oscillator (NMO) with a single spin in presence of a uniform external magnetic field. The NMO was fabricated out of single-layer graphene, grown using Chemical Vapor Deposition (CVD) and patterned using various lithography and etching techniques. The NMO was driven electrically and detected optically. The NMO's resonant frequencies, and their stabilities were studied. The spin originated from a nitrogen vacancy (NV) center in a diamond nanocrystal which is positioned on the NMO. In presence of an external magnetic field, we show that the NV centers are excellent $\theta^{2}$ sensors. Their sensitivity is shown to increase much faster than linearly with the external magnetic field and diverges as the external field approaches an internally-defined limit. Both these components of the hybrid system get coupled by physical placement of NV-containing diamond nanocrystals on top of NMO undergoing torsional mode of oscillation, in presence of an external magnetic field. The capability of the NV centers to detect the quadratic behavior of the oscillation angle of the NMO with excellent sensitivity, ensures quantum non-demolition (QND) measurement of both components of the hybrid system. This enables a bridge between the quantum and classical worlds for a simple readout of the NV center spin and observation of the discrete states of the NMO. This system could become the building block for a wide range of quantum nanomechanical devices.

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Quantum memory and non-demolition measurement of single phonon state with nitrogen-vacancy centers ensemble

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In a diamond, the mechanical vibration-induced strain can lead to interaction between the mechanical mode and the nitrogen-vacancy (NV) centers. In this work, we propose to utilize the strain-induced coupling for the quantum non-demolition (QND) single phonon measurement and memory in a diamond. The single phonon in a diamond mechanical resonator can be perfectly absorbed and emitted by the NV centers ensemble (NVE) with adiabatically tuning the microwave driving. An optical laser drives the NVE to the excited states, which have much larger coupling strength to the mechanical mode. By adiabatically eliminating the excited states under large detuning limit, the effective coupling between the mechanical mode and the NVE can be used for QND measurement of the single phonon state. Under realistic experimental conditions, we numerically simulate the scheme. It is found that the fidelity of the absorbing and emitting process can reach a much high value. The overlap between the input and the output phonon shapes can reach 98.57%.

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A fully functional quantum computer must contain at least two important components: a quantum memory for storing and manipulating quantum information and a quantum data bus to securely transfer information between quantum memories. Typically, a quantum memory is composed of a matter system, such as an atom or an electron spin, due to their prolonged quantum coherence. Alternatively, a quantum data bus is typically composed of some propagating degree of freedom, such as a photon, which can retain quantum information over long distances. Therefore, a quantum computer will likely be a hybrid quantum device, consisting of two or more disparate quantum systems. However, there must be a reliable and controllable quantum interface between the memory and bus in order to faithfully interconvert quantum information. The current engineering challenge for quantum computers is scaling the device to large numbers of controllable quantum systems, which will ultimately depend on the choice of the quantum elements and interfaces utilized in the device. In this thesis, we present and characterize a hybrid quantum device comprised of single nitrogen-vacancy (NV) centers embedded in a high quality factor diamond mechanical oscillator. The electron spin of the NV center is a leading candidate for the realization of a quantum memory due to its exceptional quantum coherence times. On the other hand, mechanical oscillators are highly sensitive to a wide variety of external forces, and have the potential to serve as a long-range quantum bus between quantum systems of disparate energy scales. These two elements are interfaced through crystal strain generated by vibrations of the mechanical oscillator. Importantly, a strain interface allows for a scalable architecture, and furthermore, opens the door to integration into a larger quantum network through coupling to an optical interface.There are a few important engineering challenges associated with this device. First, there have been no previous demonstrations of a strain-mediated spin-mechanical interface and hence the system is largely uncharacterized. Second, fabricating high quality diamond mechanical oscillators is difficult due to the robust and chemically inert nature of diamond. Finally, engineering highly coherent NV centers with a coherent optical interface in nanostructured diamond remains an outstanding challenge. In this thesis, we theoretically and experimentally address each of these challenges, and show that with future improvements, this device is suitable for future quantum-enabled applications. First, we theoretically and experimentally demonstrate a dynamic, strain-mediated coupling between the spin and orbital degrees of freedom of the NV center and the driven mechanical motion of a single-crystal diamond cantilever. We employ Ramsey interferometry to demonstrate coherent, mechanical driving of the NV spin evolution. Using this interferometry technique, we present the first demonstration of nanoscale strain imaging, and quantitatively characterize the previously unknown spin-strain coupling constants. Next, we use the driven motion of the cantilever to perform deterministic control of the frequency and polarization dependence of the optical transitions of the NV center. Importantly, this experiment constitutes the first demonstration of on-chip control of both the frequency and polarization state of a single photon produced by a quantum emitter. In the final experiment, we use mechanical driving to engineer a series of spin ``clock" states and demonstrate a significant increase in the spin coherence time of the NV center. We conclude this thesis with a theoretical discussion of prospective applications for this device, including generation of non-classical mechanical states and spin-spin entanglement, as well as an evaluation of the current limitations of our devices, including a possible avenues for improvement to reach the regime of strong spin-phonon coupling.

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Quadrature squeezing of the system consisting of nitrogen-vacancy centers in diamond coupled to cavity field and mechanical resonator

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With the great improvement of nanotechnology, it is now possible to fabricate mechanical resonator with dimension on a micro and even nanometer scale.Because of its high vibration frequency, quality factor, very small mass, and low intrinsic dissipation, nanomechanical resonator has important applications in the field of high-precision displacement detection, force detection, mass measurement, and accurate quantum computation.Mechanical resonator is also a promising candidate for observing quantum effects in macroscopic objects.By coupling nanomechanical resonator to other solid-state system such as optical cavity, microwave cavity, nitrogen-vacancy center (NV center) and superconducting qubits, researchers have successfully cooled the mechanical resonator to its quantum ground state, which paves the way for observing nonclassical states in resonator such as superposition state and Fock state.On the other hand, the nitrogenvacancy center in diamond has attracted more and more attention because of its advantages of long coherence time at room temperature, the ability to implement initialization and readout, and microwave control.Moreover, these NV centers can be used to detect weak magnetic field and electric field at room temperature.By using both laser field and microwave field, one can implement the manipulation, storage, and readout of the quantum information.In addition, because NV centers couple to both optical field and microwave field, they can also be used as a quantum interface between optical system and solid-state system.This provides a promising platform to study novel quantum phenomena based on NV centers separated by long distances.The nitrogen-vacancy center in diamond coupled to nanomechanical resonator can be used in precision measurement and quantum information processing, which has become a hot research topic.In this paper, we study the dynamics of quadrature squeezing of the phonon field in the system consisting of nitrogen-vacancy centers in diamond coupled to both cavity field and mechanical resonator.The effects of initial state of nitrogen-vacancy center and the coupling strength between nitrogen-vacancy center and mechanical resonator on the quadrature squeezing of the phonon field are analyzed.It is shown that the phonon field squeezed state with longtime and high-degree can be generated.The physical reason is that the mechanical resonator has the largest coherence.Moreover, the non-classical property of quadrature squeezing of mechanical resonator can be achieved by manipulating the initial state of nitrogen-vacancy center and magnetic field gradient.The proposal may provide a theoretical way to control and manipulate the quadrature squeezing of the phonon field.The results obtained here may have great significance and applications in the field of quantum information processing and precision measurement.

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Abstract The optical absorption spectrum of the hybrid system composed of the nitrogen-vacancy (NV) center coupled to the mechanical resonators is. investigated. Based on the pump-probe technology, the electronically induced transparency (EIT) is observed and the reasonable explanation for this transparency is given. We demonstrate that the position of the transparency is equal to the detuning difference. In addition, a completely new scheme to measure the coupling between the NV center and current carrying carbon nanotube mechanical resonator is obtained. Furthermore, an optical approach to measure the frequency of the vibrating graphene mechanical resonator is proposed. This work can provide some help for the application in the field of high-precision measurement and quantum information processing.

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We investigate the hybrid quantum system of a superconducting flux qubit, a single electronic spin associated with a negatively charged nitrogen vacancy (NV) center in diamond, and a high-quality magnetized nanomechanical resonator (NAMR). It is shown that the quantized motion of the NAMR can strongly couple to both the NV spin and the flux qubit. We estimate that the coupling strength of the NAMR to both the NV spin and the flux qubit can be about 2 π × 100 kHz, which is one order of magnitude larger than direct spin–qubit coupling. This enables the quantum state transfer to be faster and more robust against decoherence. The present work may provide an appealing way for quantum information processing based on hybrid solid-state quantum systems.

Journal of the Optical Society of America B•Nov 16, 2021•5 citations
While the motions of macroscopic objects must ultimately be governed by quantum mechanics, the distinctive features of quantum mechanics can be hidden or washed out by thermal excitations and coupling to the environment. We propose a system consisting of a graphene nanomechanical oscillator (NMO) coupled with a single spin through a uniform external magnetic field, which could become the building block for a wide range of quantum nanomechanical devices. The choice of graphene as the NMO material is critical for minimizing the moment of inertia of the oscillator. The spin originates from a nitrogen-vacancy (NV) center in a diamond nanocrystal that is positioned on the NMO. This coupling results in quantum non-demolition (QND) measurements of the oscillator and spin states, enabling a bridge between the quantum and classical worlds for a simple readout of the NV center spin and observation of the discrete states of the NMO.
Though the motions of macroscopic objects must ultimately be governed by quantum mechanics, the distinctive features of quantum mechanics can be hidden or washed out by thermal excitations and coupling to the environment. For the work of this thesis, we tried to develop a hybrid system consisting a classical and a quantum component, which can be used to probe the quantum nature of both these components. This hybrid system quadratically coupled a nanomechanical oscillator (NMO) with a single spin in presence of a uniform external magnetic field. The NMO was fabricated out of single-layer graphene, grown using Chemical Vapor Deposition (CVD) and patterned using various lithography and etching techniques. The NMO was driven electrically and detected optically. The NMO's resonant frequencies, and their stabilities were studied. The spin originated from a nitrogen vacancy (NV) center in a diamond nanocrystal which is positioned on the NMO. In presence of an external magnetic field, we show that the NV centers are excellent θ2\theta^{2}θ2 sensors. Their sensitivity is shown to increase much faster than linearly with the external magnetic field and diverges as the external field approaches an internally-defined limit. Both these components of the hybrid system get coupled by physical placement of NV-containing diamond nanocrystals on top of NMO undergoing torsional mode of oscillation, in presence of an external magnetic field. The capability of the NV centers to detect the quadratic behavior of the oscillation angle of the NMO with excellent sensitivity, ensures quantum non-demolition (QND) measurement of both components of the hybrid system. This enables a bridge between the quantum and classical worlds for a simple readout of the NV center spin and observation of the discrete states of the NMO. This system could become the building block for a wide range of quantum nanomechanical devices.
In a diamond, the mechanical vibration-induced strain can lead to interaction between the mechanical mode and the nitrogen-vacancy (NV) centers. In this work, we propose to utilize the strain-induced coupling for the quantum non-demolition (QND) single phonon measurement and memory in a diamond. The single phonon in a diamond mechanical resonator can be perfectly absorbed and emitted by the NV centers ensemble (NVE) with adiabatically tuning the microwave driving. An optical laser drives the NVE to the excited states, which have much larger coupling strength to the mechanical mode. By adiabatically eliminating the excited states under large detuning limit, the effective coupling between the mechanical mode and the NVE can be used for QND measurement of the single phonon state. Under realistic experimental conditions, we numerically simulate the scheme. It is found that the fidelity of the absorbing and emitting process can reach a much high value. The overlap between the input and the output phonon shapes can reach 98.57%.
A fully functional quantum computer must contain at least two important components: a quantum memory for storing and manipulating quantum information and a quantum data bus to securely transfer information between quantum memories. Typically, a quantum memory is composed of a matter system, such as an atom or an electron spin, due to their prolonged quantum coherence. Alternatively, a quantum data bus is typically composed of some propagating degree of freedom, such as a photon, which can retain quantum information over long distances. Therefore, a quantum computer will likely be a hybrid quantum device, consisting of two or more disparate quantum systems. However, there must be a reliable and controllable quantum interface between the memory and bus in order to faithfully interconvert quantum information. The current engineering challenge for quantum computers is scaling the device to large numbers of controllable quantum systems, which will ultimately depend on the choice of the quantum elements and interfaces utilized in the device. In this thesis, we present and characterize a hybrid quantum device comprised of single nitrogen-vacancy (NV) centers embedded in a high quality factor diamond mechanical oscillator. The electron spin of the NV center is a leading candidate for the realization of a quantum memory due to its exceptional quantum coherence times. On the other hand, mechanical oscillators are highly sensitive to a wide variety of external forces, and have the potential to serve as a long-range quantum bus between quantum systems of disparate energy scales. These two elements are interfaced through crystal strain generated by vibrations of the mechanical oscillator. Importantly, a strain interface allows for a scalable architecture, and furthermore, opens the door to integration into a larger quantum network through coupling to an optical interface.There are a few important engineering challenges associated with this device. First, there have been no previous demonstrations of a strain-mediated spin-mechanical interface and hence the system is largely uncharacterized. Second, fabricating high quality diamond mechanical oscillators is difficult due to the robust and chemically inert nature of diamond. Finally, engineering highly coherent NV centers with a coherent optical interface in nanostructured diamond remains an outstanding challenge. In this thesis, we theoretically and experimentally address each of these challenges, and show that with future improvements, this device is suitable for future quantum-enabled applications. First, we theoretically and experimentally demonstrate a dynamic, strain-mediated coupling between the spin and orbital degrees of freedom of the NV center and the driven mechanical motion of a single-crystal diamond cantilever. We employ Ramsey interferometry to demonstrate coherent, mechanical driving of the NV spin evolution. Using this interferometry technique, we present the first demonstration of nanoscale strain imaging, and quantitatively characterize the previously unknown spin-strain coupling constants. Next, we use the driven motion of the cantilever to perform deterministic control of the frequency and polarization dependence of the optical transitions of the NV center. Importantly, this experiment constitutes the first demonstration of on-chip control of both the frequency and polarization state of a single photon produced by a quantum emitter. In the final experiment, we use mechanical driving to engineer a series of spin ``clock" states and demonstrate a significant increase in the spin coherence time of the NV center. We conclude this thesis with a theoretical discussion of prospective applications for this device, including generation of non-classical mechanical states and spin-spin entanglement, as well as an evaluation of the current limitations of our devices, including a possible avenues for improvement to reach the regime of strong spin-phonon coupling.
With the great improvement of nanotechnology, it is now possible to fabricate mechanical resonator with dimension on a micro and even nanometer scale.Because of its high vibration frequency, quality factor, very small mass, and low intrinsic dissipation, nanomechanical resonator has important applications in the field of high-precision displacement detection, force detection, mass measurement, and accurate quantum computation.Mechanical resonator is also a promising candidate for observing quantum effects in macroscopic objects.By coupling nanomechanical resonator to other solid-state system such as optical cavity, microwave cavity, nitrogen-vacancy center (NV center) and superconducting qubits, researchers have successfully cooled the mechanical resonator to its quantum ground state, which paves the way for observing nonclassical states in resonator such as superposition state and Fock state.On the other hand, the nitrogenvacancy center in diamond has attracted more and more attention because of its advantages of long coherence time at room temperature, the ability to implement initialization and readout, and microwave control.Moreover, these NV centers can be used to detect weak magnetic field and electric field at room temperature.By using both laser field and microwave field, one can implement the manipulation, storage, and readout of the quantum information.In addition, because NV centers couple to both optical field and microwave field, they can also be used as a quantum interface between optical system and solid-state system.This provides a promising platform to study novel quantum phenomena based on NV centers separated by long distances.The nitrogen-vacancy center in diamond coupled to nanomechanical resonator can be used in precision measurement and quantum information processing, which has become a hot research topic.In this paper, we study the dynamics of quadrature squeezing of the phonon field in the system consisting of nitrogen-vacancy centers in diamond coupled to both cavity field and mechanical resonator.The effects of initial state of nitrogen-vacancy center and the coupling strength between nitrogen-vacancy center and mechanical resonator on the quadrature squeezing of the phonon field are analyzed.It is shown that the phonon field squeezed state with longtime and high-degree can be generated.The physical reason is that the mechanical resonator has the largest coherence.Moreover, the non-classical property of quadrature squeezing of mechanical resonator can be achieved by manipulating the initial state of nitrogen-vacancy center and magnetic field gradient.The proposal may provide a theoretical way to control and manipulate the quadrature squeezing of the phonon field.The results obtained here may have great significance and applications in the field of quantum information processing and precision measurement.
Abstract The optical absorption spectrum of the hybrid system composed of the nitrogen-vacancy (NV) center coupled to the mechanical resonators is. investigated. Based on the pump-probe technology, the electronically induced transparency (EIT) is observed and the reasonable explanation for this transparency is given. We demonstrate that the position of the transparency is equal to the detuning difference. In addition, a completely new scheme to measure the coupling between the NV center and current carrying carbon nanotube mechanical resonator is obtained. Furthermore, an optical approach to measure the frequency of the vibrating graphene mechanical resonator is proposed. This work can provide some help for the application in the field of high-precision measurement and quantum information processing.
We investigate the hybrid quantum system of a superconducting flux qubit, a single electronic spin associated with a negatively charged nitrogen vacancy (NV) center in diamond, and a high-quality magnetized nanomechanical resonator (NAMR). It is shown that the quantized motion of the NAMR can strongly couple to both the NV spin and the flux qubit. We estimate that the coupling strength of the NAMR to both the NV spin and the flux qubit can be about 2 π × 100 kHz, which is one order of magnitude larger than direct spin–qubit coupling. This enables the quantum state transfer to be faster and more robust against decoherence. The present work may provide an appealing way for quantum information processing based on hybrid solid-state quantum systems.